It's a "Right"---But Is It *right* to Allow Some, ..Not All ?

I recently seeded an article about a mother that became angry that a man was openly viewing internet porn during late afternoon hours on a Sunday in the public library such that passersby could easily view what he was watching. She was there with her two young daughters that were in the children's section, so most likely they would not have encountered the public viewers where the pornographic content was openly seen.

We all know that it is a Constitutional right to allow pornographic content to be broadcast across the internet. My question to all of you is why do we see this as a 'right' for the government, yet in private places, e.g. stores and theaters, there is an age restriction? Is that a result of private 'discretion' to have those age restrictions, or is that a government regulation? If it's a law or regulation for the private sector---isn't that government hypocrisy?